Ricci-Flat Manifolds, Parallel Spinors and the Rosenberg Index [PDF]
Symmetry, Integrability and Geometry: Methods and ApplicationsEvery closed connected Riemannian spin manifold of non-zero $\hat{A}$-genus or non-zero Hitchin invariant with non-negative scalar curvature admits a parallel spinor, in particular is Ricci-flat. In this note, we generalize this result to closed connected spin manifolds of non-vanishing Rosenberg index.
Thomas Tony
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DEGENERATIONS OF RICCI-FLAT CALABI–YAU MANIFOLDS [PDF]
Communications in Contemporary Mathematics, 2013 This paper is a sequel to [Continuity of extremal transitions and flops for Calabi–Yau manifolds, J. Differential Geom.89 (2011) 233–270]. We further investigate the Gromov–Hausdorff convergence of Ricci-flat Kähler metrics under degenerations of Calabi–Yau manifolds. We extend Theorem 1.1 in [Continuity of extremal transitions and flops for Calabi–Yau
Rong, Xiaochun, Zhang, Yuguang
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Brownian motion on Perelman’s almost Ricci-flat manifold [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 2019 Abstract We study Brownian motion and stochastic parallel transport on Perelman’s almost Ricci flat manifold ℳ = M
Esther Cabezas-Rivas, Robert Haslhofer
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Radiometric Constraints on the Timing, Tempo, and Effects of Large Igneous Province Emplacement
Geophysical Monograph Series, Page 27-82., 2021 Exploring the links between Large Igneous Provinces and dramatic environmental impact
An emerging consensus suggests that Large Igneous Provinces (LIPs) and Silicic LIPs (SLIPs) are a significant driver of dramatic global environmental and biological changes, including mass extinctions.
Jennifer Kasbohm +2 more
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The collapsing geometry of almost Ricci-flat 4-manifolds [PDF]
Commentarii Mathematici Helvetici, 2020 We consider Riemannian 4-manifolds that Gromov–Hausdorff converge to a lower dimensional limit space, with the Ricci tensor going to zero. Among other things, we show that if the limit space is two dimensional then under some mild assumptions, the limiting four dimensional geometry away from the curvature blowup region is semiflat Kähler.
John Lott
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Suberconfomal Svmmetrv and Geometrv of Ricci-Flat Kahler Manifold [PDF]
Suberconfomal Svmmetrv and Geometrv of Ricci-Flat Kahler ManifoldHirosi Ooguri
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Conformal holonomy of C-spaces, Ricci-flat, and Lorentzian manifolds [PDF]
Differential Geometry and its Applications, 2005 30 pages, revised versions: typos corrected, references added, in v4 error in Theorem 4.2 ...
Thomas Leistner
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On Bochner Flat Kähler B-Manifolds
Axioms, 2023 We obtain on a Kähler B-manifold (i.e., a Kähler manifold with a Norden metric) some corresponding results from the Kählerian and para-Kählerian context concerning the Bochner curvature. We prove that such a manifold is of constant totally real sectional
Cornelia-Livia Bejan +2 more
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A gap theorem for Ricci-flat 4-manifolds [PDF]
Differential Geometry and its Applications, 2012 Let $(M,g)$ be a compact Ricci-flat 4-manifold. For $p \in M$ let $K_{max}(p)$ (respectively $K_{min}(p)$) denote the maximum (respectively the minimum) of sectional curvatures at $p$. We prove that if $$K_{max} (p) \le \ -c K_{min}(p)$$ for all $p \in M$, for some constant $c$ with $0 \leq c < \frac{2+\sqrt 6}{4}$, then $(M,g)$ is flat.
Atreyee Bhattacharya, Harish Seshadri
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Asymptotically cylindrical Ricci-flat manifolds [PDF]
Proceedings of the American Mathematical Society, 2006 Asymptotically cylindrical Ricci-flat manifolds play a key role in constructing Topological Quantum Field Theories. It is particularly important to understand their behavior at the cylindrical ends and the natural restrictions on the geometry. In this paper we show that an orientable, connected, asymptotically cylindrical manifold
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